from manim import *
class math(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(60*2+1):       
            dot1=Dot([-500,5*(i-60),0]).set_opacity(0.5)
            dot2=Dot([500,5*(i-60),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(100*2+1):        
            dot3=Dot([(i-100)*5,-300,0]).set_opacity(0.5)
            dot4=Dot([(i-100)*5,300,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        text = Tex(r"\text{(1)}$\int \dfrac{1}{1+\cos ^{2}x}dx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,0,0])
        text1 = Tex(r"\text{(2)}$\int _{0}^{\pi }\dfrac{1}{1+\cos ^{2}x}dx$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,0,0])
        self.play(Write(text),Write(text1),self.camera.frame.animate.scale(0.8))
        self.wait()
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        self.play(text.animate().move_to([-20,20,0]) ,text1.animate().move_to([20,20,0]) )
        rectangle=Rectangle(color=BLUE,fill_opacity=0.3,width=21,height=6
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([20,20,0])
        self.play(Create(rectangle))

        arrow = Arrow(start=[20,15,0],end=[20,10,0],color=RED
                       , stroke_width=20, tip_length=1)
        text4 = Tex(r"\text{先求不定积分}",color=GREEN
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(arrow,RIGHT,buff=1)
        text5 = Tex(r"$\int \dfrac{1}{1+\cos ^{2}x}dx $"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,5,0])
        text6 = Tex(r"$=\dfrac{1}{\sqrt{2}}\arctan \left( \dfrac{\tan x}{\sqrt{2}}\right) +C$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text5,DOWN,buff=1)
        self.play(GrowArrow(arrow),Write(text4),Write(text5),Write(text6))

        arrow1 = Arrow(start=[20,-5,0],end=[20,-10,0],color=RED
                       , stroke_width=20, tip_length=1)
        text7 = Tex(r"\text{带入}$\int _{0}^{\pi }$",color=GREEN
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(arrow1,RIGHT,buff=1)
        
        text8 = Tex(r"$\dfrac{1}{\sqrt{2}}\arctan ( \dfrac{\tan x}{\sqrt{2}}) | _{0}^{\pi }=0$"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([20,-15,0])
        self.play(Write(text8),GrowArrow(arrow1),Write(text7))
        rectangle1=Rectangle(color=RED,fill_opacity=0.3,width=3,height=3
                            ,stroke_color=RED,stroke_width=20)
        rectangle1.move_to([33.3,-15,0])
        self.play(Create(rectangle1))
        self.play(FadeOut(rectangle))
        self.play(Create(rectangle))
        text9 = Tex(r"$x=\dfrac{\pi }{2}$",color=GREEN
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-6,-1.5,0])
        arrow2 = Arrow(start=[-1,-1.5,0],end=[4,-1.5,0],color=BLUE
                       , stroke_width=20, tip_length=1)
        self.play(Write(text9),GrowArrow(arrow2))

        rectangle2=Rectangle(color=RED,fill_opacity=0.2,width=30,height=6
                            ,stroke_color=RED,stroke_width=20)
        rectangle2.next_to(text5,DOWN,buff=1)
        self.play(Create(rectangle2))
        text10 = Tex(r"$\dfrac{1}{\sqrt{2}}\arctan \left(  \frac{\tan x}{\sqrt{2}}\right)  | _{0}^{\left( \frac{\pi }{2}\right) ^{-} }+\dfrac{1}{\sqrt{2}}\arctan \left(  \frac{\tan x}{\sqrt{2}}\right)  | _{\left( \frac{\pi }{2}\right) ^{+} }^{\pi}$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-8.5,0])
        self.play(ReplacementTransform(rectangle2,text10))
        self.wait(0.2)
        text11 = Tex(r"$=\dfrac{\pi }{\sqrt{2}}$",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text10,DOWN,buff=1)
        self.play(Write(text11))
        self.wait()